Finite Group Databasebeta

← Group #10824911

Character table — Group #10824911

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212128888888888882424242424242424242424242424242424242424242424242444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1111-1-111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-11-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-11111-1-1-1-1
χ91111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111111-1-1-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-111
χ111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-11-1-111-1-111
χ121111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111-111-1-111-1-1
χ131111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111
χ141111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-11111-1-1
χ151111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-1-11111111-1-1
χ161111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1111111-1-1-1-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ202222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ26222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ27222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ28222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-111111111-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-2222-2-222-2-222-2-22222222-2-222-2-222-2-2-2-200000000000000000000000000000000000022-20000-200000000
χ302222-2-2222-2-222-2-222-2-22222222-2-222-2-222-2-2-2-2000000000000000000000000000000000000-2-220000200000000
χ312222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-2-2-22222000000002-22-2000000000000000022-2-222-2-20000000000000000
χ322222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-2-2-2222200000000-22-220000000000000000-2-222-2-2220000000000000000
χ332222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-222000000002-2-22000000000000000022-2-2-2-2220000000000000000
χ342222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-22200000000-222-20000000000000000-2-22222-2-20000000000000000
χ352222-2-22-2-222-2-22222-2-22222222-2-2-2-222-2-222-2-20000000000000000000000000000000000002-220000-200000000
χ362222-2-22-2-222-2-22222-2-22222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000-22-20000200000000
χ372222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-1000000002-22-233−3−333−3−333−3−333−3−3-1-111-1-1110000000000000000
χ382222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-1000000002-22-2−3−333−3−333−3−333−3−333-1-111-1-1110000000000000000
χ392222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-100000000-22-2233−3−333−3−3−3−333−3−33311-1-111-1-10000000000000000
χ402222-2-2-122-2-2-2-222-2-222-1-1-1111111-1-11111-1-1-1-100000000-22-22−3−333−3−33333−3−333−3−311-1-111-1-10000000000000000
χ412222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-1000000002-2-2233−3−3−3−33333−3−3−3−333-1-11111-1-10000000000000000
χ422222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-1000000002-2-22−3−33333−3−3−3−33333−3−3-1-11111-1-10000000000000000
χ432222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-100000000-222-233−3−3−3−333−3−33333−3−311-1-1-1-1110000000000000000
χ442222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-100000000-222-2−3−33333−3−333−3−3−3−33311-1-1-1-1110000000000000000
χ452-2-222-222i−2i2i−2i2i−2i2i−2i2-22-22-2-222-2-22-22i−2i2i−2i2i−2i2i−2i2-2000000000000000000000000000000000000000002i−2i0002-20000
χ462-2-222-222i−2i2i−2i2i−2i2i−2i2-22-22-2-222-2-22-22i−2i2i−2i2i−2i2i−2i2-200000000000000000000000000000000000000000−2i2i000-220000
χ472-2-222-222i−2i2i−2i−2i2i−2i2i-22-222-2-2-2-2222-22i−2i2i−2i−2i2i−2i2i-222i−2i2-2000000002i−2i2i−2i2-22-200000000000000000000000000000000
χ482-2-222-222i−2i2i−2i−2i2i−2i2i-22-222-2-2-2-2222-22i−2i2i−2i−2i2i−2i2i-22−2i2i-2200000000−2i2i−2i2i-22-2200000000000000000000000000000000
χ492-2-222-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2-2-2222-2−2i2i−2i2i2i−2i2i−2i-222i−2i-22000000002i−2i2i−2i-22-2200000000000000000000000000000000
χ502-2-222-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2-2-2222-2−2i2i−2i2i2i−2i2i−2i-22−2i2i2-200000000−2i2i−2i2i2-22-200000000000000000000000000000000
χ512-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i2-2000000000000000000000000000000000000000002i−2i000-220000
χ522-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2-22-2−2i2i−2i2i−2i2i−2i2i2-200000000000000000000000000000000000000000−2i2i0002-20000
χ532-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-12i−2i2-200000000−ii−ii-11-11−i3i3−i3i33−33−33−33−3−i3i3−i3i30000000000000000
χ542-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-12i−2i2-200000000−ii−ii-11-11i3−i3i3−i3−33−33−33−33i3−i3i3−i30000000000000000
χ552-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-1−2i2i-2200000000i−ii−i1-11-1−i3i3−i3i33−33−3−33−33i3−i3i3−i30000000000000000
χ562-2-222-2-12i−2i2i−2i−2i2i−2i2i-22-22-11111-1-1-11−ii−iii−ii−i1-1−2i2i-2200000000i−ii−i1-11-1i3−i3i3−i3−33−333−33−3−i3i3−i3i30000000000000000
χ572-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-12i−2i-2200000000−ii−ii1-11-1−i3i3−i3i3−33−333−33−3i3−i3i3−i30000000000000000
χ582-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-12i−2i-2200000000−ii−ii1-11-1i3−i3i3−i33−33−3−33−33−i3i3−i3i30000000000000000
χ592-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-1−2i2i2-200000000i−ii−i-11-11−i3i3−i3i3−33−33−33−33−i3i3−i3i30000000000000000
χ602-2-222-2-1−2i2i−2i2i2i−2i2i−2i-22-22-11111-1-1-11i−ii−i−ii−ii1-1−2i2i2-200000000i−ii−i-11-11i3−i3i3−i33−33−33−33−3i3−i3i3−i30000000000000000
χ612-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-222-2-2-222i−2i−2i2i2i−2i−2i2i-2200002i−2i2-20000000000002i−2i−2i2i-222-2000000000000000000000000
χ622-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-222-2-2-222i−2i−2i2i2i−2i−2i2i-220000−2i2i-22000000000000−2i2i2i−2i2-2-22000000000000000000000000
χ632-2-22-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2-2-222-222i−2i−2i2i−2i2i2i−2i2-20000000000000000000000000000000000000002i−2i0002-2000000
χ642-2-22-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2-2-222-222i−2i−2i2i−2i2i2i−2i2-2000000000000000000000000000000000000000−2i2i000-22000000
χ652-2-22-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2-2-222-22−2i2i2i−2i2i−2i−2i2i2-20000000000000000000000000000000000000002i−2i000-22000000
χ662-2-22-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2-2-222-22−2i2i2i−2i2i−2i−2i2i2-2000000000000000000000000000000000000000−2i2i0002-2000000
χ672-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-222-2-2-22−2i2i2i−2i−2i2i2i−2i-2200002i−2i-220000000000002i−2i−2i2i2-2-22000000000000000000000000
χ682-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-222-2-2-22−2i2i2i−2i−2i2i2i−2i-220000−2i2i2-2000000000000−2i2i2i−2i-222-2000000000000000000000000
χ692-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-100002i−2i2-20000−i3i3i3−i3−333−3−iii−i1-1-11−333−3i3−i3−i3i30000000000000000
χ702-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-100002i−2i2-20000i3−i3−i3i33−3−33−iii−i1-1-113−3−33−i3i3i3−i30000000000000000
χ712-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-10000−2i2i-220000−i3i3i3−i3−333−3i−i−ii-111-13−3−33−i3i3i3−i30000000000000000
χ722-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111-1-1111-1−iii−i−iii−i1-10000−2i2i-220000i3−i3−i3i33−3−33i−i−ii-111-1−333−3i3−i3−i3i30000000000000000
χ732-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-100002i−2i-220000−i3i3i3−i33−3−33−iii−i-111-1−333−3−i3i3i3−i30000000000000000
χ742-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-100002i−2i-220000i3−i3−i3i3−333−3−iii−i-111-13−3−33i3−i3−i3i30000000000000000
χ752-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-10000−2i2i2-20000−i3i3i3−i33−3−33i−i−ii1-1-113−3−33i3−i3−i3i30000000000000000
χ762-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111-1-1111-1i−i−iii−i−ii1-10000−2i2i2-20000i3−i3−i3i3−333−3i−i−ii1-1-11−333−3−i3i3i3−i30000000000000000
χ77444444-24444-4-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ78444444-2-4-4-4-44444-4-4-4-4-2-2-22222-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ794444-4-4-244-4-444-4-444-4-4-2-2-2-2-2-2-222-2-222-2-222220000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-444-4-44444-4-4-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ814-4-444-4-24i−4i4i−4i4i−4i4i−4i4-44-4-222-2-222-22−2i2i−2i2i−2i2i−2i2i-220000000000000000000000000000000000000000000000000000
χ824-4-444-4-2−4i4i−4i4i−4i4i−4i4i4-44-4-222-2-222-222i−2i2i−2i2i−2i2i−2i-220000000000000000000000000000000000000000000000000000
χ834-4-44-44-24i−4i−4i4i−4i4i4i−4i-444-4-22222-2-22-2−2i2i2i−2i2i−2i−2i2i-220000000000000000000000000000000000000000000000000000
χ844-4-44-44-2−4i4i4i−4i4i−4i−4i4i-444-4-22222-2-22-22i−2i−2i2i−2i2i2i−2i-220000000000000000000000000000000000000000000000000000
χ8588-8-8008000000000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-40000000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-8008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-800-400000000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-400000000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).